Methods and systems for applying genetic operators to determine system conditions

ABSTRACT

Disclosed are methods, systems, and/or processor program products that include generating a population of genotypes, the genotypes based on at least one stimulus to a system, measuring at least one response of the system upon providing the population of genotypes to at least one model of the system, and, based on the measured at least one response of the system, performing at least one of: (a) applying at least one genetic operator to at least some of the population of genotypes, and iteratively returning to generating a population of genotypes, and (b) associating a condition of the system with at least one of the population of genotypes.

CLAIM OF PRIORITY

This application claims priority to the following provisional patentapplications, the entireties of which are expressly incorporated hereinby reference: U.S. Ser. No. 60/491,864 filed on Aug. 1, 2003, U.S. Ser.No. 60/537,761 filed on Jan. 20, 2004, U.S. Ser. No. 60/543,195 filed onFeb. 10, 2004, and U.S. Ser. No. 60/585,631, entitled “Hacker simulationmodel: Evolving Hacker Scripts,” filed on Jul. 6, 2004

RELATED APPLICATIONS

This application is related to co-pending U.S. Ser. No. 10/815,321,filed on Apr. 1, 2004, the contents of which are expressly incorporatedherein by reference in their entirety.

BACKGROUND

(1) Field

The disclosed methods and systems relate generally to evolutionarycomputing (EC), and more particularly to EC as related to system controland/or modeling.

(2) Description of Relevant Art

Evolutionary Algorithms (EA) can be used in solving and/or approximatingsolutions to multifaceted problems, and/or problems that may change overtime. In some embodiments, evolutionary algorithms can generally beunderstood to include stochastic search methods that replicate naturalbiological evolution. Accordingly, use of EAs is predicated on anability to parameterize possible solutions to a problem using a datastructure upon which genetic operations can be performed. Those ofordinary skill understand that Genetic Algorithms are an instance of EAsin which the data structure includes a fixed-length list of values(e.g., single bit), where such data structure elements can be referredto as “genes.”

Often, evolutionary algorithms operate on a population of potentialsolutions by applying a “survival of the fittest” principle to produceapproximations to a solution, and includes evaluating potentialsolutions against a prescribed and/or specified objective or fitnessfunction. A new solution set of approximations is thus created at eachgeneration by selecting potential solutions (“individuals”) according totheir level of “fitness” in the problem domain (i.e., identifying thosebest approximating the specified fitness function), and breeding theseselected “individuals” using operators emulating natural genetics. Sucha process facilitates an evolution of populations of “individuals” thatare better suited to their environment than the individuals that theywere created from, just as in natural adaptation.

Evolutionary algorithms can thus model natural processes includingselection, recombination, mutation, migration, locality, andneighborhood. Evolutionary algorithms are generally performed in aparallel manner, using for example, a migration, global, or diffusionmodel, to operate on populations of individuals rather than singlesolutions/individuals. Accordingly, a solution set of individuals (e.g.,population) can be randomly initialized, and an objective or fitnessfunction can be evaluated for these individuals. If optimizationcriteria are not satisfied, a new generation is created whereindividuals are selected according to their fitness for the productionof offspring. Parents can be recombined to produce offspring, andoffspring can be mutated with a certain probability. The fitness of theoffspring is then computed, and the offspring replace the parents in thepopulation to provide a new generation. This cycle is performed untilthe optimization criteria are satisfied (e.g., satisfying an errorcriteria between one or more solutions, and the fitness/objectivefunction).

In systems having a large number of control parameters, for example, itmay not be possible to encode, describe, or otherwise fully evaluate thespace of possible system configurations due to the large number ofcontrol parameters.

SUMMARY

Disclosed are methods, systems, and/or processor program products thatinclude generating a population of genotypes, the genotypes based on atleast one stimulus to a system, measuring a response(s) of the systemupon providing the population of genotypes to a model(s) of the system,and, based on the measured response(s) of the system, performing atleast one of: (a) applying a genetic operator(s) to at least some of thepopulation of genotypes, and iteratively returning to generating apopulation of genotypes, and (b) associating a condition of the systemwith at least one of the population of genotypes. The geneticoperator(s) can include one or more of selection, crossover, mutation,deletion, diversity injection, and elitism.

The methods and systems can include implementing elitism by presentingat least two graphical representations to a user, each of the at leasttwo graphical representations associated with at least one genotype inthe population and at least one of the measured response(s), receiving aselection of at least one of the graphical representations, and,identifying at least one genotype associated with the at least oneselected graphical representation, where, in the methods' and systems'returning to generating a population of genotypes, the methods andsystems include the identified genotype in the next generation of thepopulation of genotypes.

In some embodiments, implementing elitism includes comparing themeasured response(s) to a measure, and, based on the comparison,identifying at least one genotype, and, where, in the methods' andsystems' returning to generating a population of genotypes, the methodsand systems include the identified genotype in the next generation ofthe population of genotypes.

In associating a condition of the system with at least one of thepopulation of genotypes, the methods and systems can compare themeasured response(s) to a threshold(s), and, determine the conditionbased on the comparison. Further, in measuring the response(s) of thesystem, the methods and systems can compare the measured response(s) toa metric that can be a fitness function and/or an objective function.

In some embodiments, a fitness function/objective function may not beknown, and may be mathematically unexpressed. In such embodiments, themethods and systems can include determining that an objective functionis mathematically unexpressed, presenting data based on the measuredresponse(s) of the system to at least one user, receiving at least oneinput from the user(s), the input(s) based on the user(s)'s evaluationof the presented data. The user(s)'s input can include, for example, oneor more of: a rank of the measured response(s), a rating of the measuredresponse(s), one or more fitness values, a selection of the measuredresponse(s), a selection of a feature of the measured response(s), atermination of the method, an identification of parents for a geneticalgorithm, at least one constraint, a modification of at least oneconstraint, a modification of at least one genetic operator, and aspecification of at least one genetic operator. In some embodiments, themethods and systems can be terminated based on the user(s)'s input(s).

In embodiments, measuring the response(s) of the system can includepresenting data based on the measured response(s) in parallel and/or insequential order, to the user(s).

Applying a genetic operator(s) can also include ranking the measuredresponse(s) based on a comparison to a metric, and, applying the geneticoperator(s) based on the ranking, where applying can include applying atleast one constraint to at least one of the genotypes. Applyingconstraints can include weighting the constraints.

It can thus be understood that the methods and systems can be used todetermine and/or associate a system condition with the response, wherethe system condition can include one or more of: an unknown systemvulnerability(s), a system error(s), a system defect(s), a systemloophole(s), and/or a system weakness(es).

Other objects and advantages will become apparent hereinafter in view ofthe specification and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram of one embodiment of the disclosed methods andsystems;

FIG. 2 provides a schematic of a hydraulic model for a horizontal loopfiremain system;

FIG. 3 demonstrates chromosomal crossover for the example firemainembodiment;

FIG. 4 illustrates genic crossover for the example firemain embodiment;

FIG. 5 illustrates mutation for the example firemain embodiment;

FIG. 6 shows a schematic of a hydraulic network for a pipe rupture insixty-three locations;

FIG. 7 illustrates the results of one simulation;

FIG. 8 illustrates webs of webpages;

FIG. 9 illustrates computation of a web page score;

FIG. 10 illustrates four GOOGLE bombs;

FIG. 11 illustrates a hacker script grammar;

FIG. 12 provides examples of chromosome scripts;

FIG. 13 shown one example of a subset of a script gene pool;

FIG. 14 provides an example of an elitism operation;

FIG. 15 illustrates a diversity injection operation;

FIG. 16 illustrates a crossover operation;

FIG. 17 illustrates a mutation operation;

FIG. 18 illustrates a gene subtraction operation;

FIG. 19 illustrates a determination of a next generation;

FIG. 20 illustrates top scorers for a hacker simulation experiment;

FIG. 21 illustrates top scorers for a second hacker simulationexperiment; and,

FIG. 22 represents a GUI for interactive evolution.

DESCRIPTION

To provide an overall understanding, certain illustrative embodimentswill now be described; however, it will be understood by one of ordinaryskill in the art that the systems and methods described herein can beadapted and modified to provide systems and methods for other suitableapplications and that other additions and modifications can be madewithout departing from the scope of the systems and methods describedherein.

Unless otherwise specified, the illustrated embodiments can beunderstood as providing exemplary features of varying detail of certainembodiments, and therefore, unless otherwise specified, features,components, modules, and/or aspects of the illustrations can beotherwise combined, separated, interchanged, and/or rearranged withoutdeparting from the disclosed systems or methods. Additionally, theshapes and sizes of components are also exemplary and unless otherwisespecified, can be altered without affecting the scope of the disclosedand exemplary systems or methods of the present disclosure.

The disclosed methods and systems include various EA embodiments thatcan be employed for testing a model/system, where a model can beunderstood herein to be a representation of a device and/or system,and/or a component(s) thereof. Accordingly, a model can include asimulation, for example, and the system being modeled can include acontrol system, a software system, a hardware system, an econometricsystem, and/or another system for which a model can be provided. Thedisclosed methods and systems for testing the model can include methodsand systems for discovering characteristics of the model/system,including vulnerabilities that may otherwise be unknown, system errors,defects, loopholes, and/or other weaknesses, where such examples areprovided for illustration and not limitation. In an embodiment, thediscovery and/or search for such model/system characteristics can employsubjective data/input that can be provided by, for example, a user.

In one embodiment, the disclosed methods and systems can be understoodto employ evolutionary schemes and agent-based modeling (ABM) tofacilitate the evolution of scenarios to test and challenge systems suchas control systems. In such embodiments, the methods and systems can beused to determine, locate, search for, and/or discover combinations ofcontrol system parameters from among a population of possible controlsystem actions, which cause the control system to behave, for example,in undesirable manners. Identifying such control system combinationsprovides information regarding system weaknesses, defects, etc.

In one embodiment, a control system can be tested prior to reduction topractice, implementation, installation, and/or integration, although themethods and systems can similarly be applied to existing (control)systems. Some examples of a control system include the digital controlsystem of an automobile or a computer network, where often complexarrangements of electronic and mechanical systems frequently employlarge numbers of sensors to gather data to determine how to modulateoutput behavior.

Generally, a control system is provided and/or presented withconfigurations of parameters (e.g., sensor data), whereupon the controlsystem processes such data and thereafter provides output controlbehavior. Using the output-behavior as an objective function, thedisclosed methods and systems can search a space of input/stimulusparameter data to provide the control system with a configuration ofparameter data. The process can iterate to identify parameterconfigurations that provide undesirable control system behavior. Byexploring the space of possible input/stimulus and output behaviors, amore robust control system design may be achieved. The number ofiterations can be user-determined, and may depend upon the size of thecontrol system. It can be understood that varying types of systembehaviors can be identified, including desirable, undesirable, etc., andaccordingly, references to determination of “undesirable” behavior canbe understood to be an example of one category of systemcharacteristics, where the disclosed methods and systems are not limitedto such category.

In some embodiments, different types of data can be evolved to discoversystem conditions. For example, the methods and systems can beunderstood to include embodiments for evolving static input data,dynamic input data, static system/environmental configurations, dynamicsystem/environmental configurations, open-ended sequence and/or parallelsequences of system commands, adaptive agents, and/or co-evolving dataand system response/correction.

An Agent-based Model (ABM) is a computer simulation of agents thatparticipate in a system where an individual agent can assess itssituation and can make decisions based upon a set of rules, andtherefore an ABM can be based on a system of agents and the associatedrelationships between agents. Agents can execute various behaviors basedon the system(s) which the agents represent (e.g., producing, consuming,selling, with such examples provided for illustration and notlimitation). It can be understood that an ABM can exhibit complexbehavior patterns and hence may provide information about the dynamicsof the system that the ABM emulates. The system can be an actual (e.g.,“real-world”) system, or a theoretical system.

An Evolutionary Algorithm (EA) can be understood to be a stochasticsearch method that can be applied to a population of solutions. Asprovided herein, EA (and more specifically, genetic algorithms (GA)and/or genetic programming (GP)) can generally include three factorsthat include: a population of solutions that may be randomlyinitialized, one or more mutation operators capable of altering and/orchanging at least one of the solutions to a neighboring solution (e.g.,a local search operator), and a recombination operator which canrecombine a genotype of two parents into a child solution inheritingtraits from both parents (e.g., a global search operator). Recombinationcan include reproduction, mutation, and/or crossover, where crossovercan be understood to be the combination of two individuals (the“parents”) to produce two more individuals (the “children”). Someembodiments may employ elitism. Those of ordinary skill will recognizethat crossover can include asexual crossover and/or single-childcrossover. Accordingly, crossover can be understood to provide geneticmaterial from a previous generation to a subsequent generation. Mutationintroduces randomness to the process. The variations of EA are thus wellknown in the art, and the disclosed methods and systems are not limitedby such implementations and/or variations of embodiments.

Although in some EA applications, a solution can be obtained bycomparing individual solutions to a pre-determined objective and/orfitness function, in some of the disclosed embodiments, the objectiveand/or fitness function is not pre-determined, but rather, is defined,designated, and/or otherwise selected by a user during iterations and/orepochs of the EA. Further, as provided herein, a solution is not basedon individual solutions (e.g., agents), but rather, a solution can bebased on a user-input that can be based on a user-evaluation of thecollective population (e.g., swarm). The disclosed methods and systemsthus allow for a collective evaluation of the population by a user,rather than an individual evaluation of population constituents againstan objective function. It can be understood that the disclosed methodsand systems may not include an objective function, but rather, asubjective evaluation of the collective behavior.

In one embodiment of the disclosed methods and systems that is providedfor illustration and not limitation, an ABM is created to replicate asystem of interacting components whose control system is represented bya set of rules that governs the behavior and interaction between thecomponents, and where the system level properties are measured andreported by the ABM. The ABM is exposed to a combination ofenvironmental and system input parameters and the outcomes are observedat the systemic level. EA methods are then used to search the space ofinput parameter data based on the observed outputs of the ABM, untilcombinations of input parameters are identified that lead to asearched-for behavior(s) of interest, which may include, for example, anindication of robustness of the underlying control system.

In such an embodiment, the methods and systems may apply evolutionarytechniques where the objective function is a priori unspecified, anddetermined subjectively by a user via the disclosed methods and systems,based on input(s) from the user(s). Whether the objective function(otherwise known as a fitness function) is a priori unknown, incomplete,susceptible to change, and/or a priori unexpressed mathematically, suchconditions can be referred to herein collectively as “a priorimathematically unexpressed.”

Accordingly, although in some EA applications, a solution can beobtained by comparing individual solutions to a pre-determined objectiveand/or fitness function, in some embodiments of the disclosedembodiments, the objective and/or fitness function is not pre-determinedand/or otherwise entirely known (i.e., it is a priori mathematicallyunexpressed), but rather, such fitness function can be defined,designated, and/or otherwise obtained using the disclosed methods andsystems, via user(s) input(s) during iterations and/or epochs of the EA.The user(s) input(s) can be of the type mentioned herein (e.g.,modifying EA parameters, assigning rank, modifying components offitness/constraints).

Because, in some embodiments, the “search” for a solution can be basedon user(s) input(s), the disclosed methods and systems can allow forseveral parallel and/or sequential representations of the possiblesolutions identified in each EA/GA/GP iteration to be visually presentedto one or more users. Accordingly, one or more users can be presented(e.g., graphical user interface, display, etc.) with several paralleland/or sequential representations of solutions, and the ability toprovide user input via selection tools and modification mechanisms(e.g., sliders, entry boxes, selection/drop-down boxes, etc.). Thedifferent users may be provided such solutions at a singleprocessor-controlled device, and/or such users may be connected tomultiple processor-controlled devices, for example, over a network. Themethods and systems thus contemplate a stand-alone and/or distributedmulti-user environment that can include one or more client-serverrelationships. For example, a user can assign fitness values to thevarious solutions according to the perceived value or interestingness ofthe solutions presented to such user. In an embodiment, the user-deemedhighest fitness solutions can be selected to make a new generation ofoffspring solutions, borrowing from the multiplicity of thecharacteristics in the such user-selected fitness solutions. In amulti-user embodiment, fitness values (and/or other inputs) assigned bythe users can be aggregated to the solutions. Aggregation can beperformed by weighting fitness values based on the user, and/or applyingequal weights to users. For example, user(s) input(s) (e.g., additionalconstraints and/or other inputs) may be weighted based on the identity,status, etc., of the user (e.g., a supervisor may be provided moreweight than a non-supervisor.). In one embodiment, fitness values(and/or other inputs) can be weighted based on a user's response time.Those of ordinary skill in the art will recognize that there are manydifferent aggregation and/or weighting mechanisms that can be employed,and the disclosed methods and systems are not limited by suchvariations.

In some embodiments, multiple users may be given an interval of time inwhich to respond, and if a response is not received from a given user(s)within the time interval, such user's input(s) may not be employed toobtain a new solution set. The user may or may not be informed of thetime interval. In some embodiments, a user's input(s) may be used eventhough such input(s) was based on a previous generation, and thus, basedon the foregoing, the disclosed methods and systems can be understood toallow for asynchronous input of users.

Although the described methods and systems can contemplate a human user,a user can include a non-human user that can be configured with apattern-recognition mechanism. For example, one embodiment can employmachine vision or other pattern recognition concepts to identify adetermined pattern, and cause a selection of a parallel embodiment asprovided herein. In some embodiments, visual representations mayadditionally and/or optionally include not only the agents' collectivebehavior pattern, but data representing properties and/orcharacteristics of the collective behavior (e.g., physical and/or otherproperties, statistical measures, statistical plots, etc.).

FIG. 1 shows one example embodiment of the disclosed methods and systemsthat uses interactive evolutionary computing (IEC), although as providedherein, other embodiments do not employ an optional interactivecomponent. In the FIG. 1 embodiment, based on the embodiment (e.g., thedesign being considered, the problem to be addressed, etc.), primitivessuch as objectives, constraints, fitness evaluation criteria, etc., canbe developed 110, and upon which a population of solutions can bedeveloped 112 (e.g., using a genetic algorithm). The solutions can beapplied to the data 114 applicable to the embodiment, and at least someof the solutions, and/or data based upon such solutions (e.g., plots,property, characteristic, collective behavior, etc.), can be provided toone or more users 116 for visual inspection. The user can thereafterprovide input based on the user's preferences 118, which as providedherein, can be subjective to the user(s), and can include apreference/selection, a ranking, an additional constraint, amodification of a constraint, a selection of a parent, and/or anotheruser input allowed by the embodiment. In the FIG. 1 embodiment, the userinput is generally a ranking. Based on the user's input, geneticoperations can be performed 120 and a new population generated 112. Theexample process of FIG. 1 can continue until a user(s) determines that asolution is obtained 122. Those of ordinary skill will understand thatthe example method and system of FIG. 1 can be rearranged, as providedherein, and for example, can include user input at other additionaland/or optional places in the processing.

Accordingly, in applying FIG. 1 to the disclosed methods and systemswhich can be related to a model of a system and using an EA/GA/GP todiscover characteristics of the system, primitives 110 may be related tosystem/model parameters and/or inputs, and may be related to particularof such parameters and/or inputs that are believed to be of interest toand/or related to the characteristic of interest. Based on theseprimitives, a population can be formed 112 to provide an input to thesystem (e.g., control system) 114. In one embodiment, the population canbe representative of sensor data and/or system conditions, for example.The output of the system model, in the illustrated embodiment of FIG. 1,can be displayed to a user(s) 116 who may select one or more of theoutputs 118, where such selections may be viewed as a selection withrespect to an elitism operator. Genetic operators can then be applied120 as specified in the embodiment to generate a new population 112. Itcan be understood that in other embodiments, display to the user(s) 116and/or user(s) selection 118 may not be performed the GA/EA/GP, butrather, a user and/or another (e.g., system administrator) may determinea priori a scheme (e.g., compute a fitness score for each population,select a percentage of the population per elitism based on the fitnessscore, and perform genetic operations on the remainder of thepopulation). In the FIG. 1 embodiment, a user input may determine whenthe methods and systems may end 122, although it can be understood thatother metrics (e.g., computational values) can be used optionally and/oradditionally in some embodiments.

In one example embodiment, the disclosed methods and systems were usedto test local controls that open and close valves and controls that turnpumps on and off on a ship's firemain. Such a system, an example ofwhich is shown in FIG. 2, includes a hydraulic network of pumps, valves,pressurized pipes, and sprinkler heads. In the example embodiment, valveand pump control logic was fixed, and a genetic algorithm was used toevolve two types of system characteristics and/or challenges: first,“extrinsic challenges” such as pipe rupture, e.g. a result of enemyattack, and second, intrinsic challenges such as water drawn off thesystem, e.g. for ballasting.

In a desired “controlled” system, the valve controls isolate sections ofruptured pipe, thereby stemming local flooding while maintaining flow tothe sprinkler heads and to junctions where water may need to be drawnoff, e.g. to fill ballast tanks thus preventing list. Also, pumps shouldshut off if they are pumping into “dead ends” and/or to ruptured pipe.

In such a system, there are thus several interdependencies. For example,sprinkler head outflow is based on hydraulic pressure which is based onwater demand that may occur in distant sections of the network. Also,valve closure can divert and increase flow to sections of the ship whilecurtailing it to others.

In the example embodiment, a model was provided with thirteen sprinklerheads that occur in the real ship (FIG. 2, s1-s13) which are evenlyspread across the firemain, and an implementation that includedthirty-one stop valves (FIG. 2, SV1-SV31) with local, controlling logic.Also included in the model are six pumps, each operating with thefollowing head-flow pump curve: head=533.34−0.0001334×flow2. In “normal”operation for the model, such operation produces approximatelytwo-hundred thirty pounds per square inch pressure.

Ruptures, which can be a virtual hole in the pipe with a constantemitter coefficient, may occur at sixty-three locations (FIG. 2,r1-r63), where each location represents a particular between-valve pipein the network. Further, water demands, expressed as a constant outflowin gallons per minute (gpm) from a junction, may occur at any offorty-nine locations around the ship.

In the example embodiment, valve and control logic included thefollowing provisions: if a pipe ruptures, every “local” stop valvecloses to isolate the broken pipe from the network. In one case, if apipe ruptures, two stop valves close at either end of the pipe toprevent flow into that rupture location which would cause localflooding. In other cases where a rupture occurs close to a T-junction,three or four stop valves may close. Additionally, control logic isimplemented on the pumps. Accordingly, if the aforementioned controllogic closes a stop valve on the riser from a pump, the pump operationshould cease to prevent the pumping of water into a “dead end.”

In one embodiment, EPANET, a commercially available system for modelinghydraulic and water quality behavior of water distribution pipingsystems, was employed to implement the mathematics to determine thesteady state flows and pressures, the control logic of the various stopvalves and pumps, and the ruptures and demands, although the methods andsystems are not limited to such an embodiment. Using EPANET, one canspecify a pressured pipe network to include a number of pumps,reservoirs, tanks, valves, etc., and add control logic to components ofthe network.

Also developed was a C++ library known as OOTEN (Object-Oriented Toolkitfor EPANET) that acts as a “wrapper” to an EPANET simulation byfacilitating the introduction of run-time changes to the network, andobtaining the pertinent information, e.g. state, flow, pressure, etc. ofcomponents of the network.

In such an embodiment, each genotype, i.e., scenario parsed to an EPANETsimulation, includes two chromosomes: an r-chromosome represented by abit string that encodes rupture (or not) at each of the sixty-threepipes; and, a d-chromosome represented by a bit string that encodes awater demand (or not) at each of the forty-nine possible locations. Anindividual genotype, i, can thus be represented by its respective r- andd-chromosomes using the index i and the notation such that r_(i) andd_(i), respectively, and the j^(th) gene of the i^(th) chromosomes canbe represented as as r_(i,j) and d_(i,j).

In the example embodiment, provided herein, the GA includes threegenetic operators: chromosomal crossover, genic crossover, and mutation.Chromosomal crossover is illustrated in FIG. 3, and indicates that themating of two parents, r₁d₁ and r₂d₂, causes the swapping orinterchanging of the r- and d-chromosomes to produce two new offspring:r₁d₂ and r₂d₁.

Generally, an unconstrained GA will evolve to a worst case scenario,which in the present embodiment, would include a scenario in which allpipes ruptured and all water was siphoned (r_(i,j)=d_(i,j)=1 ∀ i, j).Accordingly, the number of pipe ruptures was held constant to a numberN_(r)<<63, and the number of water demands was also held constant to anumber N_(d)<<49.

Further, the traditional GA crossover operator was modified. Given ther-chromosome of two parents, a and b, then for each locus, j∈{1 . . .63}, the gene values of the two parents are compared. If the gene valuesmatch, e.g., r_(a,j)=r_(b,j), then swapping is meaningless as offspringcannot differ from their parents with respect to gene j. Accordingly,the locations in which the gene values do not match and/or differ areidentified (e.g., r_(a,j)≠r_(b,j)). The two difference scenarios can betermed a “−locus” (e.g., r_(a,j)=0 and r_(b,j)=1) or a “+locus” (e.g.,r_(a,j)=1 and r_(b,j)=0). Regardless of the chromosome's length, theparity of N_(r) and N_(d), and the number of locations with matchinggene values, the number of −loci and +loci will be equal (as long asN_(r) is the same for both parents). Accordingly, the loci can berandomly paired (without replacement) so that one locus of the pair is a−locus and the other locus is a +locus (e.g., a form of random geneticlinkage). For each of these ±loci pairings, with probability 0.5, genevalues (0→1 and 1→0) are swapped, as shown in FIG. 4.

Rupture locations can be defined by a symmetric proximity matrix, M_(r),where an entry M_(ri,j) specifies the physical distance (in 2D Euclideanspace) between two rupture locations i and j. An existing rupture on ther-chromosome is randomly selected, e.g., some j where r_(i,j)=1. Avector

$W = {{1/M_{r,i,j}}/{\sum\limits_{i = 1}^{49}\;{1/M_{{ri},j}}}}$specifies normalized weightings that are inversely proportional to theEuclidean distance between rupture locations i and j. W is used toselect a new rupture location, e.g., k, probabilistically. Thereafter,r_(i,j)=0 and r_(k,j)=1, thus preferentially rupturing a nearby locationinstead of j (See FIG. 5). Similarly, the d-chromosome is mutated usingan appropriate proximity matrix, M_(d), that gives the physicaldistances between the water demand locations. It is because ruptures anddemands involve different proximity matrices that two chromosomes pergenotype are employed in this illustrative embodiment.

In one such embodiment, the fitness function can be based on twometrics: deadwater length, and maximum pump flow. Deadwater lengthincludes the total length of pipe, in feet, with zero flow, whichincludes sections of pipe that are isolated from the pumps due to closedstop valves, and sections that are “dead ends” (i.e., no outlet).Further, the maximum pump flow can be expressed in gallons per minute,for the six pumps. It can be understood that both metrics are maximandsto allow for a search of worst case performance. For simplicity, it canbe assumed that thirteen sprinklers are associated with valuesindicating “open” where water flow through the network is monitored.

Each generation of the GA included generating a population of ngenotypes, where each population was executed on a separate EPANETsimulation and the fitness of that genotype determined. To create thenext generation, elitist selection identified e “fittest” genotypesselected to pass, unaltered, into the next generation. The remainder ofthe population of the next generation, including (n-e) genotypes, wasfilled by selecting individuals of the current generationprobabilistically, weighted by their fitness.

In determining the weights, it can be supposed that the ith genotype hasfitness f_(i) and that there is a population of n such genotypes. First,a range of fitnesses R=max{f_(i)}−min{f_(i)} is determined from thepopulation. Second, a linear transformation is performed such that theminimum fitness is zero (e.g., subtract min{f_(i)} from each f_(i) suchthat fitnesses range from zero to R). It can be understood that inembodiments where it may be desired to minimize the fitness metric, Rcan be subtracted from all fitness values. Thirdly, cR is added to eachfitness, where cε(0, ∞) and is a constant, and thus, all fitnesses rangefrom cR to (1+c)R). In this embodiment, selection occursprobabilistically from the transformed fitnesses, where c determines“selection pressure.”

After an individual is selected for the next generation, chromosomal andgenic crossover and mutation are performed with a fixed, independentprobability. In the example embodiment, these operators are notperformed on the e elites.

In an example embodiment where population size (n) is fifty, elite poolsize (e) is ten, number of generations ranges between one-hundred andthree-hundred, number of ruptures (N_(r)) is between one and five,number of demands (Nd) is between zero and two, chromosomal crossoverprobability is 0.5, genic crossover probability is 0.5, mutationprobability is 0.5, and selection pressure (c) is one, and each piperupture included a hole in a pipe with an effective emitter coefficientof two (e.g., outflow (in gpm)=2×pressure^(0.5)). Each demand alsoincluded 500 gpm drawn off a junction (excepting section 3.3).

To assess the relative importance of the sixty-three rupture locations,each of the sixty-three locations was ruptured and the outcome observedafter the control logic intervened. FIG. 6 shows the dead water length,in feet, after a rupture in each of the sixty three rupture locations.For example, a pipe rupture in the starboard aft quarter (bottom left,FIG. 6), caused approximately two-hundred thirty feet of pipe to havezero flow. FIG. 6 thus indicates that some of locations on the starboardbeam have small effects, while others have comparatively large effects,e.g. portside bow and quarter. FIG. 6 also indicates that there is notone single worst rupture location in this embodiment, but rather fourequally bad. A GA executed with a single rupture (N_(r)=1; N_(d)=0)finds and retains the four worst rupture locations in the population.

In exploring dual ruptures (N_(r)=2; N_(d)=0), there is variation withsixteen “equally worst” combinations. The GA optimizes the dead waterlength to find the same worst case scenarios. In this case, thepopulation at the end of one-hundred generations contained six of thesixteen worst scenarios.

In exploring triple ruptures (N_(r)=3; N_(d)=0), the state space islarge, and includes 63×62×61=238266 combinations, and while thesimulation executed for hours, the GA found the same maximal dead waterlength in a minutes, utilizing a median of forty-nine generations(thirty-five replicates), thus searching approximately one percent ofthe state space.

In one application of this embodiment of the disclosed methods andsystems, state space regions can be determined. For example, under whichconditions do all pumps work within particular user-defined safetylimits? In which region do pumps operate at maximal speed or pressure(e.g., for emergency situations and short periods only)? In which regiondo conditions exceed component limits? Based on these example regions ofinterest, thresholds can be determined. For example, pump flowthresholds of >1000 gpm can indicate overheating, >1250 gpm can indicatewarning/emergency operation, and >1500 can indicate dangerousconditions/untenable operation. These thresholds can be set in the GAwhich can search the state space. When the GA encounters a scenariowhose fitness exceeds the lowest threshold, it records and/or stores acopy of the genotype (and associated fitness). At the end of thesimulation, a crude map of the boundary for a user-desired threshold canbe determined. To prolong the GA's search and to avoid convergence, highvalues (e.g., one) can be set for the crossover and mutationprobabilities.

One simulation includes two ruptures, two demands of two-thousand gpmeach, and a single threshold of one-thousand gpm for pump flow, with theGA fitness metric as maximum pump flow, and values of one for the threecrossover and mutation probabilities. The two ruptures can likelyshut-down one pump each, but the four remaining pumps can work up to1500 gpm each, thus with the 2×2000 water drawn off, there should be4×1500−2×2000=2000 gpm spare capacity from the working pumps. Theresults are illustrated in FIG. 7.

FIG. 7 illustrates structure in the central-level group which indicatesseveral demand locations where water should not be drawn off duringdamage control operations. Second, the maximum pump flows are 4000 gpm,which is greater than the aforementioned analysis. The high pump flowvalues indicate that the two ruptures effectively cooperated to isolatethe fore-most pump without shutting it off. The two demands wereimmediately in front of the pump so that the 4000 gpm total demand wentimmediately from the pump to the demand locations.

This embodiment thus illustrates that a threshold search collates caseswhose fitness exceeds a user-defined threshold(s), thereby allowing moreinvolvement in the testing process. Accordingly, in an embodiment, thescenario generation can be interactive. In such an embodiment, a usercan be presented with a panel of variants and can select/identify, etc.one or more for mating in the next generation, thus biasing anddirecting the GA towards certain regions of state space. For greatercontrol and influence, a user may want to fix certain features of thescenario interactively (e.g., always draw water from a specificlocation) while allowing the other ruptures and demands to evolve. Forexample, the key locations identified by threshold search in FIG. 7 canbe fixed with other conditions evolved to understand why suchdisproportionate failure occurs with these demand locations.

In another embodiment of the disclosed methods and systems, EA/GA can beapplied to vulnerabilities in, for example, a search engine. Forexample, the term “GOOGLE bombing” is associated with the GOOGLE searchengine, and is known to be a technique to establish a significant numberof web pages with links to a given website so as to affect the GOOGLEranking of the website and cause that website to appear near the top ofa GOOGLE search results page. Accordingly, is some instances, the searchterm does not appear in the website, yet the website appears near thetop of a results page for the search term. It is thus understood thatweb page linkers can affect the “page score” of linkees, where a pagescore is understood to affect the overall ranking, and thus placement,of the website/webpage in the results list.

In such an embodiment, the disclosed methods and systems can be used toevolve GOOGLE bombs in a simulated network of webpages to evaluate thosestrategies, if any, that generate a situation in which a target page iselevated to the top of a search result without a given search termappearing in the target page. The disclosed methods and systems can thususe a genetic algorithm to mutate and otherwise evolve populations ofwebs.

In simulating webs of simplified webpages, each webpage includes a maintext which includes a string of uppercase characters representing themain content text of a web page. The page also includes a set of HTMLlinks that each contain a link text (generally also a string ofuppercase characters, but limited in this embodiment to a singlecharacter), and a link ID that points to a web page having the given ID.FIG. 8 demonstrates these webpage features.

With reference to FIG. 8, “B6” represents an HTML link containing thelink text “B” and links to webpage 6. A link ID of 0 represents anon-link, which also includes a manner of evolving the number ofoutgoing links in a page. In an initial model of one embodiment, awebpage includes a main text having five characters and five HTML links,each with a single character. Ten webpages linked according to theirHTML links form a web. Webpage #1 is understood to be the targetwebpage.

As indicated herein, each webpage can be associated with a page rankwhich is a numerical value indicating the webpage's “importance.” In oneembodiment, page rank can be computed as provided by Equation (1):

$\begin{matrix}{{{{PR}(i)} = {\left( {1 - d} \right) + {d\left( {\frac{{PR}\left( t_{1} \right)}{C\left( t_{1} \right)} + \frac{{PR}\left( t_{2} \right)}{C\left( t_{2} \right)} + \ldots + \frac{{PR}\left( t_{n} \right)}{C\left( t_{n} \right)}} \right)}}},} & (1)\end{matrix}$where PR(i) is the page rank of webpage i, d is a damping factor thatcan be a constant (e.g., 0.85), t_(j) is a webpage j that links towebpage i, and C(t_(j)) is the number of outbound HTML links fromwebpage j. Equation 1 can be re-written as shown in Equation (2), andsolved simultaneously for all webpages in the web using numericaltechniques such as Gaussian elimination, although other embodiments mayemploy other techniques.

$\begin{matrix}{{\begin{pmatrix}{d - 1} \\{d - 1} \\\vdots \\{d - 1}\end{pmatrix} = {\begin{pmatrix}{- 1} & {+ \frac{d \times L_{1,2}}{C_{2}}} & {+ \frac{d \times L_{1,3}}{C_{3}}} & \cdots & {+ \frac{d \times L_{1,n}}{C_{n}}} \\\frac{d \times L_{2,1}}{C_{1}} & {- 1} & {+ \frac{d \times L_{2,3}}{C_{3}}} & \cdots & {+ \frac{d \times L_{2,n}}{C_{n}}} \\\vdots & \; & \; & \; & \vdots \\\frac{d \times L_{n,1}}{C_{1}} & {+ \frac{d \times L_{n,2}}{C_{2}}} & \cdots & {+ \frac{d \times L_{n,{n - 1}}}{C_{n - 1}}} & {- 1}\end{pmatrix}\begin{pmatrix}P_{1} \\P_{2} \\\vdots \\P_{n}\end{pmatrix}}}{{{where}\mspace{14mu} L_{i,j}} = \left\{ {\begin{matrix}1 & {{if}\mspace{14mu}{webpage}\mspace{14mu} j\mspace{20mu}{links}\mspace{20mu}{to}\mspace{14mu} i} \\0 & {otherwise}\end{matrix}.} \right.}} & (2)\end{matrix}$

A webpage's page score can be understood to be a numeric valueassociated with a given search term. Such a score can be based onvarious webpage characteristics, features, and/or properties, includingfor example, location and font size of the keywords and links, pagetitle, and page rank. In one embodiment, page score can be determined byassociating each webpage with a bar chart which incorporates thefrequency of words (e.g., upper case characters) that appear in the webpage, and also, the text (e.g., single upper case characters) thatappear in the HTML links that link into the webpage. These twoproperties can be weighted differently such that each character of awebpage is given a weight of one, while characters from incoming linksare weighted by the page rank of the webpages sending out the links. Forexample, if a simulated Web page includes main text “ACDIJ” and has HTMLlinks B6, Q2, Z2, and K0, the associated bar chart can includecategories A, C, D, I, J, B, Q, Z, K each with frequency one (differentembodiments may or may not incorporate K which is a non-link). Further,if it is assumed that only a single web page links into a focal page,and in the present embodiment, such single page includes text “K” andthat webpage's page rank is 1.5. Accordingly, “K” can be added to thebar chart, which already has a category K, but further, the frequency ofK can increase by the page rank by 1.5, providing a frequency for K of1+1.5=2.5 (FIG. 9).

Once a bar chart has been calculated for a webpage, the webpage's scorefor a given search term can be computed. In the illustrated embodiment,a search term can be understood as including three upper casecharacters, for example, “DJK.” The frequencies can be combined (e.g.,summed) from the barchart for each of the characters in the search term,thus DJK is the sum of 1 (i.e., frequency of D)+1 (i.e., frequency ofJ)+1.5 (i.e., frequency of K), for a final score of 3.5. Duplicatecharacters are counted such that a score for search term “JKK” is1+1.5+1.5=4. In an example embodiment including simulations, the term“ICO” was used.

The page score for each webpage in a web can be computed and the GOOGLEbomb that is formed is a target page having the highest page score whilenot containing the search term in its text, i.e., the page score is aresult of the incoming links rather than the page text (content).

This example embodiment used a GA/EA to evolve a population of webs andsearch for GOOGLE bombs in the network state space of the ten Web pageshaving five main text characters and five single character HTML linksweb, thereby providing a state space of size (26⁵×26⁵×11⁵)¹⁰≈3.7×10¹⁹³(11 HTML link webIDs ranging from 0-10 inclusive). In the example case,the genotype corresponded to the webpage text and links IDs. In thisillustrative, example, the disclosed systems and methods includegenerating a population of n separate webs, and calculating the pagescores of the Web pages in the webs for the same search term of“ICO.”The fitness of each web was determined and associated with afitness value, and based on the fitness values, a number e of webs waschosen to pass unaltered into the next generation. The remaining (n-e)“selected” webs can be altered using fixed probability, geneticoperators.

In an initial mode of one embodiment, the example systems and methodsimplement mutation operators only, although the disclosed systems andmethods are not so limited. For example, recombination operators can beimplemented in other models. Three separate mutation operators wereimplemented in the illustrative systems/methods, operating in a similarmanner. For mutations on main text in a web, there is a main textmutation probability p_(M)∈(0, 1) and a main text mutation level,n_(M)∈{1,2, . . . , ∞}. Binomial(n_(M), p_(M)) web pages are selected atrandom, and for each selected webpage, one of the main text charactersis selected at random and mutated to a random upper case character.Hence, between zero and nM characters may be mutated. Similarly, formutations on HTML link text in a web, there is a link text mutationprobability p_(L)δ(0, 1) and a main text mutation level, n_(L)∈{1,2, . .. , ∞}. Binomial(n_(L), p_(L)) web pages are selected at random, and foreach selected webpage, one of the HTML links is selected at random andits text mutated to a random upper case character. For mutations of HTMLlink IDs, there is a link ID mutation probability p_(I)∈(0, 1) and amain text mutation level, n_(I)∈{1,2, . . . , ∞}. Binomial(n_(I), p_(I))web pages are selected at random, and for each selected webpage, one ofthe HTML links is selected at random and its ID mutated to a randomnumber between zero (no link) and the number of web pages in a web.

For the illustrated embodiment, two objectives can be incorporated intothe fitness function: first, webs are fitter if the target webpage doesnot include the search term in their main or HTML link text; and,second, the fitter the webs, the higher the target page's page scorerelative to the other pages in the web. These two aspects are includedas a “mismatch score” and “target page rank,” respectively.

The aforementioned mismatch score, in one example, can range betweenzero (e.g., all characters of the search term appear in the target webpage) and one (e.g., there is no match between the search term and thetarget page's text). Suppose the search term includes s characters, andthe number of these characters that appear in the target webpage isa∈{0,1, . . . , s}:Mismatch score=(s−a)/s.  (3)

A second factor in the fitness, target page rank, can be determinedafter the page scores are computed, as target page rank can be thenumber of webpages in a given web having a page score less than that ofthe target webpage. Hence for w Web pages that constitute a web, themaximum target page rank value is w−1 if the target has the highest pagescore, and zero if the target page has the lowest score or all pageshave the same score.

In the disclosed embodiment,Fitness=mismatch score×target page rank.  (4)

The example embodiment can consider the fitness value(s) provided hereinas a raw fitness, and accordingly, selection for the next generation canbe based not on these values but on weightings representing a normalizedselection pressure. Suppose the i^(th) web has fitness f₁. A range offitnesses R=max{f}−min{f} is determined, and a linear transformation canbe performed such that the minimum is zero (e.g., subtract min{f} fromeach f₁, so that fitness ranges from zero to R). Once again, inembodiments where it may be desired to minimize a fitness metric, R canbe subtracted from all fitness values. Thereafter, (c×R) can be added toeach fitness where c∈(0, ∞) and is a constant, thereby scaling thefitness range from cR to (1+c)R. Selection can occur probabilisticallyfrom these transformed fitnesses, where c determines “selectionpressure.”

TABLE 1 typical parameter values used in the simulations. ParameterValue Population size, n 100 Elite size, e  5 Maximum generations 150Number of web page in a web  10 Selection pressure, c  0.5 Main textlength  5 (upper case characters only) Number HTML links  5 Link textlength  1 (upper case characters only) Target page ID  1 Search term“ICO” Main text mutation probability, p_(M)  0.25 Main text mutationlevel, n_(M)  2 Link text mutation probability, p_(L)  0.25 Link textmutation level, n_(L)  2 Link ID mutation probability, p_(I)  0.25 LinkID mutation level n_(I)  2

Table 1 provides parameter values used in one embodiment. The exampleembodiment coded a utility in “R” that plots the “anatomy” of a GOOGLEbomb, i.e., the network link structure, and shown in FIG. 10. Eachnumber 1-10 represents a Web page. The target page is in bold and alsoindicated with an asterisk, and arrows represent the HTML links. Linksto the target page are also shown in bold. The lack of a pattern maysuggest that there may exist a large number of strategies to GOOGLE bomba target page.

In other embodiments of the GA, techniques other than Gaussianelimination can be used. Further, although the present embodimentincluded initial conditions that were completely randomized and the GAwas free to mutate different text and link IDs with equal probability,other variations may bias initial HTML link text to the characters ofthe search term, increase the length of the link text, bias links to thetarget page, specify that any link to the target page must containcharacters in the search term, make links to the target “sticky,” i.e.,less likely to mutate than other links, and, optimize the parametervalues.

In another embodiment of the disclosed methods and systems, a geneticalgorithm (GA/EA) and interactive evolution can be used to evolvescripts to explore the space of possible intrusions to a computersystem. Using the disclosed methods and systems, vulnerabilities of thecomputer system can be identified. For the disclosed embodiments, theintrusions can be understood to be in the form of scripts by anunauthorized user, referred to herein and generally as a “hacker.”

Accordingly, the model of the disclosed embodiment can include twodifferent types of agents, authorized users (“users”) and hackers, andthe operating environment, or a server. As is known, users interact withthe server by regularly logging in and out and performing other userbehavior once on the system (e.g., run programs, applications, generatecode, add and modify files and/or directories, FTP files to and from theserver, etc.). Conversely, a hacker generally interacts with thesystem/server by entering at random times and executing a pre-definedscript, then leaving the system. The hacker generally enters thesystem/server as a root user or as a normal user, who then uses the “su”command to become root.

User actions, including hacker actions, are captured by thesystem/server through log files and file statistics. These records canprovide evidence of the intruder.

A hacker script can be understood to be a sequence of commands that thehacker issues upon logging into the system/server. Scripts can beunderstood to be pre-defined in that they can be created before thehacker enters the server but are randomly generated using a simplegrammar. The grammar is designed such that generally, every command isprovided to achieve a goal, e.g., the theft of a file, the introductionof a “backdoor” mechanism that allows the hacker to gain entry to thesystem in the future, etc. Many of these goals can be subsumed underother goals. This subsumption tree can be used to generate a script bybeginning at the most general goals at the top and then randomlydeciding which possible sub-goals should be attempted, and how. Thisincludes recursively traversing the tree, from sub-goal to sub-goal,until concrete commands are chosen. Sub-goals can be specified either asa sequence, a combination, or a single choice picked from a list. Itemsin a sequence are executed in order, while a combination can return asubset of its items and in any order, creating the most variability.When items are specified in a list, only a single item is returned.

As an example, part of a sub-goal tree is illustrated in FIG. 11. In theFIG. 11 embodiment, the top-level goals are a sequence of entering thesystem, “doing stuff” as provided in FIG. 11, cleaning up, and exiting.As indicated in FIG. 11, “doing stuff” may include downloading a client,stealing files, creating a backdoor, and/or destroying files. A hackerscript can include one or more of these actions, performed in differentorders. Further traversing the FIG. 11 tree illustrates that creating abackdoor is another combination, which involves at least one choice,between removing /etc/hosts or /etc/hosts.deny.

An analysis program, referred to herein as the “log analyzer,” iscapable of gathering evidence from a server/computer after a simulationconcludes. Gathering evidence can include collecting raw log file dataand/or using rules to determine which out of twenty-eight pre-definedpieces of evidence a hacker left behind. These rules involve scanninglog files, the directory tree, and the statistics of key files.

Table 2 is an illustration of a relationship between basic hackeractions, log files, and a detection scheme of the log analyzer.

TABLE 2 How the Type of Elements that can be hacker can Hacker commandsdetected by the log clean up those Action involved Analyzer elementsRoot login login over ssh, entry in no cleaning telnet var_log_wtmp,scheme var_log_lastlog implemented Su to root su root entry incleanMessages /var/log/messages Download ftp - get - mv entry inbash_history cleanHistory Program Backdoor - ftp - get - mv entry inbash_history cleanHistory trojan Backdoor - echo > inetd.conf inetdmodified no cleaning inetd scheme implemented Backdoor - echo > passwd -entry in no cleaning add user echo > shadow /var/log/messages schemeimplemented Backdoor - rm hosts - rm absence of files no cleaning removehost hosts.deny scheme file implemented Steal file ftp - putbash_history cleanHistory Destroy file rm passwd - rm absence of filesno cleaning inetd.conf - rm scheme index.html implemented Clean upcleanHistory - no detection scheme cleanHistory cleanMessagesimplemented

The ScriptBuilder is a grammar that enables the creation of novelhacking scripts. The disclosed methods and systems can be employed toenhance the capabilities of a grammar such as ScriptBuilder.

In the GA/EA of the present embodiment, the population includes scripts.One script is one individual, and an individual is represented by achromosome, which is represented by a sequence of genes. Because ahacking script includes a sequence of Unix commands, a gene can bedefined as a single Unix command; however, because the length of thescripts are variable, the chromosomes length is also variable.

The gene pool can be defined as a complete set of Unix commands (FIG.12) that can be generated by ScriptBuilder; and, a chromosome caninclude an ordered subset of the gene pool (FIG. 13).

The initial population can be generated by ScriptBuilder to provide apopulation of consistent hacking scripts. A fitness function can beunderstood to be a measure of the efficiency of the hacking script, andmay use a simulation engine to assign a numeric value to one individual.

The evolutionary mechanism can utilize the genetic operators of elitism,mutation, crossover, gene subtraction, and/or diversity injection, withsuch examples provided for illustration and not limitation.

In the illustrated embodiment, two genetic operators apply to thepopulation as a whole: the elitism operator extracts, for a givengeneration, the “top” individuals with regard to their fitness, andinserts these “top” individuals in the next generation. An illustrationof elitism is shown in FIG. 14.

A diversity injection operator adds new individuals to a givenpopulation. These new individuals are generated by ScriptBuilder, andthe operation is illustrated in FIG. 15.

The crossover operator is a binary operator that creates a new childindividual, given a two parent individual. Crossover selects a firstpoint in the first parent's chromosome, and all the genes before thefirst point are given to/replicated in the child's chromosome. Crossoverthen picks a second point in the second parent's chromosome, and all thegenes after the second point are added to/replicated in the child'schromosome. FIG. 16 is representative of crossover.

The mutation operator is a unary operator in which the genes of theparent are considered individually, and there is a fixed probability(e.g., 0.05) that the gene will be mutated. If the gene is mutated, arandom gene is selected from the gene pool to replace the parent's gene.When all genes are considered, a new individual is created. FIG. 17illustrates mutation.

The gene subtraction operator is intended to make chromosomes shorter.In gene subtraction, a random number of genes (e.g., between one andfive) located at random places on the chromosome, are deleted. Deletioncreates a new individual, as shown in FIG. 18.

Given generation n as a collection of p individuals, generation n+1 isobtained using a process as shown in FIG. 19.

For example, assuming the “top” individuals are those m having the toptwenty percent fitness values, or m=p/5. Elitism is thus used toselected the m top individuals that move to generation n+1 withoutalternation. The remaining operators, parent individuals are chosenusing a selector function that can select a random individual among thehalf best of generation n.

Accordingly, m individuals are selected, and mutation is applied to themsuch that generation n+1 includes 2m individuals. Crossover is performedm times (e.g., select two parents and cross them), to provide generationn+1 has 3m individuals. Gene subtraction is performed to m selectedindividuals, to yield 4m individuals in generation n+1; and, theremaining m individuals of generation n+1 are generated by using adiversity injection operator, providing a population of p individuals ingeneration n+1. The fitness is evaluated, and the process can berepeated.

In the illustrated embodiment, a fitness function can include ameasure/measurement of the efficiency of the hacking script. To evaluatethis measure/value, the script can be provided to a simulation and thehacker activity monitored to determine when the script has reached thedifferent goals that the hacker can achieve. Also monitored are thehacker's Unix commands, specifically, to note when they return aninvalid result. When the simulation is complete, the log analyzer can beused.

Some indicators included in the fitness function include a number ofgoals achieved by the hacker (#g), a number of evidences discovered bythe log analyzer (#e), a number of bad commands used by the hacker (#b),and, a length of the script used by the hacker (#c).

In a first experiment (“experiment 1” described herein), the examplefitness function provided a fitness of zero if the hacker achieved zerogoals, and if the hacker achieved at least one goal, the fitness valueis determined according to the following:[1/(1+#e²)]*[1/(1+#b)]*[1/(1+#c/10)]  (5)Based on Equation (5), the example fitness decreases with the number ofevidences detected by the log analyzer, with the number of invalidcommands, and with the global length of the script. The fitnessincreases with a short script that leaves no trace, and has no badcommands. Such a script is the most efficient that we can achieve in thecontext of the simulation.

In a first experiment known as “experiment 1”, using one-hundred fiftyindividuals, the genetic algorithm was iterated for two-hundred andthirteen generations. The fitness function included values as providedherein relative to Equation (5). FIG. 20 presents the top scorers forgenerations one-hundred and generation two-hundred and thirteen, whichindicate little difference in identifying the script providing the “bestfitness”, which are those scripts to which the server/system is mostvulnerable. The scripts shown in FIG. 20 are thus similar in providing ascenario in which a hacker is a user, becomes a root, uploads file.rhosts to a remote server (steal file), cleans the messages file toremove the trace of the su command, and cleans the bash_history file. AsFIG. 20 indicates, the script at generation two-hundred and thirteen isshorter and more efficient. Further, the scripts of FIG. 20 cannot begenerated solely by the ScriptBuilder.

In a second experiment, the GA executed for sixty-seven generationsbased on a population of one-hundred fifty individuals. The fitnessfunction was based on Equation (6):fitness=(#g/4.0)*1.0/(1+#e)²*1.0/(1+#b)*1.0/(1.0+#c/10);  (6)where:

-   (#g)=number of goals achieved by the hacker;-   (#e)=number of evidences discovers by the log analyzer;-   (#b)=number of bad commands used by the hacker; and,-   (#c)=length of the script used by the hacker.

As FIG. 21 indicates, and with comparison to experiment 1, FIG. 20, the“top scorer” is similar. It can be understood that “scorer #6” can beevolved further to remove some commands such as the chmods, but achievesseveral goals of the same type (e.g., several backdoors). Once again,such a script cannot be generated by the Script Builder alone.

It can be understood that the foregoing examples are merelyillustrative, and that other embodiments are contemplated, for example,by providing fitness functions that measure the efficiency of a scriptbased on a (minimal) number of bad commands, favoring short scripts byincluding the length of the script in the fitness function, etc.Further, other genetic operators could be considered, such as switching(e.g., switching to genes is comparable to switching two Unix commands,and could be a complement to mutation). Additionally and/or optionally,a human/user-derived fitness function can be possible, with interactiveevolution (IE) to generate hacking scripts. Such a system is illustratedin FIG. 22, in which a Graphical User Interface can be used to display apopulation (e.g., fifteen individuals: fifteen scripts). For each of thedisplayed individuals, the simulator is executed, and the followinginformation, for example, can be displayed and/or otherwise providedwith the script/individual: number of bad commands, number of goals thatthe hacker has reached, and, number of evidences detected by the loganalyzer, where in the displayed embodiment, the color used to displaythe information reflects the number of evidences. A goal is to obtainzero evidences.

As FIG. 22 also indicates, a user can select which individual bestestimates the desired, subjective fitness by selecting one or moreindividuals. The selected individuals can be the parents of thefollowing generation, thereby satisfying elitism portion of the GA.Further, as also shown in FIG. 22 (right side), the user can decidewhich operators will be applied to the selected individuals. In someembodiments, as provided herein, although a fitness may be known, a usermay still select one or more individuals as the parents of the followinggeneration.

What has thus been described are methods, systems, and/or processorprogram products that include generating a population of genotypes, thegenotypes based on at least one stimulus to a system, measuring at leastone response of the system upon providing the population of genotypes toat least one model of the system, and, based on the measured at leastone response of the system, performing at least one of: (a) applying atleast one genetic operator to at least some of the population ofgenotypes, and iteratively returning to generating a population ofgenotypes, and (b) associating a condition of the system with at leastone of the population of genotypes.

The methods and systems described herein are not limited to a particularhardware or software configuration, and may find applicability in manycomputing or processing environments. The methods and systems can beimplemented in hardware or software, or a combination of hardware andsoftware. The methods and systems can be implemented in one or morecomputer programs, where a computer program can be understood to includeone or more processor executable instructions. The computer program(s)can execute on one or more programmable processors, and can be stored onone or more storage medium readable by the processor (including volatileand non-volatile memory and/or storage elements), one or more inputdevices, and/or one or more output devices. The processor thus canaccess one or more input devices to obtain input data, and can accessone or more output devices to communicate output data. The input and/oroutput devices can include one or more of the following: Random AccessMemory (RAM), Redundant Array of Independent Disks (RAID), floppy drive,CD, DVD, magnetic disk, internal hard drive, external hard drive, memorystick, or other storage device capable of being accessed by a processoras provided herein, where such aforementioned examples are notexhaustive, and are for illustration and not limitation.

The computer program(s) can be implemented using one or more high levelprocedural or object-oriented programming languages to communicate witha computer system; however, the program(s) can be implemented inassembly or machine language, if desired. The language can be compiledor interpreted.

As provided herein, the processor(s) can thus be embedded in one or moredevices that can be operated independently or together in a networkedenvironment, where the network can include, for example, a Local AreaNetwork (LAN), wide area network (WAN), and/or can include an intranetand/or the internet and/or another network. The network(s) can be wiredor wireless or a combination thereof and can use one or morecommunications protocols to facilitate communications between thedifferent processors. The processors can be configured for distributedprocessing and can utilize, in some embodiments, a client-server modelas needed. Accordingly, the methods and systems can utilize multipleprocessors and/or processor devices, and the processor instructions canbe divided amongst such single or multiple processor/devices.

The device(s) or computer systems that integrate with the processor(s)can include, for example, a personal computer(s), workstation (e.g.,Sun, HP), personal digital assistant (PDA), handheld device such ascellular telephone, laptop, handheld, or another device capable of beingintegrated with a processor(s) that can operate as provided herein.Accordingly, the devices provided herein are not exhaustive and areprovided for illustration and not limitation.

References to “a microprocessor” and “a processor”, or “themicroprocessor” and “the processor,” can be understood to include one ormore microprocessors that can communicate in a stand-alone and/or adistributed environment(s), and can thus can be configured tocommunicate via wired or wireless communications with other processors,where such one or more processor can be configured to operate on one ormore processor-controlled devices that can be similar or differentdevices. Use of such “microprocessor” or “processor” terminology canthus also be understood to include a central processing unit, anarithmetic logic unit, an application-specific integrated circuit (IC),and/or a task engine, with such examples provided for illustration andnot limitation.

Furthermore, references to memory, unless otherwise specified, caninclude one or more processor-readable and accessible memory elementsand/or components that can be internal to the processor-controlleddevice, external to the processor-controlled device, and/or can beaccessed via a wired or wireless network using a variety ofcommunications protocols, and unless otherwise specified, can bearranged to include a combination of external and internal memorydevices, where such memory can be contiguous and/or partitioned based onthe application. Accordingly, references to a database can be understoodto include one or more memory associations, where such references caninclude commercially available database products (e.g., SQL, Informix,Oracle) and also proprietary databases, and may also include otherstructures for associating memory such as links, queues, graphs, trees,with such structures provided for illustration and not limitation.

References to a network, unless provided otherwise, can include one ormore intranets and/or the internet. References herein to microprocessorinstructions or microprocessor-executable instructions, in accordancewith the above, can be understood to include programmable hardware.

Unless otherwise stated, use of the word “substantially” can beconstrued to include a precise relationship, condition, arrangement,orientation, and/or other characteristic, and deviations thereof asunderstood by one of ordinary skill in the art, to the extent that suchdeviations do not materially affect the disclosed methods and systems.

Throughout the entirety of the present disclosure, use of the articles“a” or “an” to modify a noun can be understood to be used forconvenience and to include one, or more than one of the modified noun,unless otherwise specifically stated.

Elements, components, modules, and/or parts thereof that are describedand/or otherwise portrayed through the figures to communicate with, beassociated with, and/or be based on, something else, can be understoodto so communicate, be associated with, and or be based on in a directand/or indirect manner, unless otherwise stipulated herein.

Although the methods and systems have been described relative to aspecific embodiment thereof, they are not so limited. Obviously manymodifications and variations may become apparent in light of the aboveteachings. For example, it can be understood that the genetic operationscan be multiple and/or varied, and different parameters associated withsuch genetic operations can be provided as input by a user/expert.Further, although user input was specified in the illustratedembodiments of FIGS. 1 and 2 as occurring at a certain instance, inputfrom the user can be provided at multiple stages (e.g., atinitialization, problem definition, etc.). Further, the disclosedembodiments can employ the use of randomly generated solutions inaddition to those derived from user selection. In multi-userembodiments, for example, the formulation of the solution can bepartitioned amongst several users, with different users influencing thesolution in a different manner. For example, an employee(s) may providesubjective input on solutions, however a manager(s) may apply/specify(additional) constraints on such solutions.

Any additional changes in the details, materials, and arrangement ofparts, herein described and illustrated, can be made by those skilled inthe art. Accordingly, it will be understood that the following claimsare not to be limited to the embodiments disclosed herein, can includepractices otherwise than specifically described, and are to beinterpreted as broadly as allowed under the law.

1. In a computer system having at least one user interface including atleast one output device and at least one input device, a method fordetermining a vulnerability of a system external to the computer system,comprising: a) receiving through at least one of the at least one inputdevices input with respect to a plurality of parameters relating to theexternal system; b) based upon the input received, generating in thecomputer system a population of genotypes, the genotypes based on atleast one stimulus to the external system, c) measuring at least oneresponse of the external system upon providing the population ofgenotypes to at least one model of the external system, d) based on themeasured at least one response of the external system not revealing avulnerability of the external system, applying at least one geneticoperator to at least some of the population of genotypes, and e) basedon the measured at least one response of the external system revealing avulnerability of the external system, associating the said vulnerabilityof the external system with at least one of the population of genotypes,and causing the said vulnerability to be presented to at least one userthrough at least one of the at least one output devices.
 2. A methodaccording to claim 1, where applying at least one genetic operatorincludes applying at least one of: selection, crossover, mutation,deletion, diversity injection, and elitism.
 3. A method according toclaim 1, where applying at least one genetic operator includesimplementing elitism by: through at least one of the at least one outputdevices, presenting at least two graphical representations to at leastone of the at least one users, each of the at least two graphicalrepresentations associated with at least one genotype in the populationand the at least one of the measured responses, through at least one ofthe at least one input devices, receiving a selection of at least one ofthe graphical representations from at least one of the at least oneusers, and, identifying at least one genotype associated with the atleast one selected graphical representation, and returning to generatinga population of genotypes including the identified at least onegenotype.
 4. A method according to claim 1, where applying at least onegenetic operator includes implementing elitism by: comparing themeasured at least one response to a measure, and, based on thecomparison, identifying at least one genotype, and, returning togenerating a population of genotypes including the identified at leastone genotype.
 5. A method according to claim 1, where based on themeasured at least one response of the external system revealing avulnerability of the external system, associating the said vulnerabilityof the external system with at least one of the population of genotypesincludes: comparing the measured at least one response to at least onethreshold, and, determining the vulnerability based on the comparison.6. A method according to claim 1, where measuring at least one responseof the external system includes comparing the measured at least oneresponse to a metric.
 7. A method according to claim 1, where measuringat least one response of the external system includes comparing themeasured at least one response to at least one of a fitness function andan objective function.
 8. A method according to claim 1, where measuringat least one response of the external system includes: determining thatan objective function is mathematically unexpressed, through at leastone of the at least one output devices, presenting data based on themeasured at least one response of the external system to at least one ofthe at least one users, and, through at least one of the at least oneinput devices, receiving at least one input from the at least one of theat least one users, the at least one input based on the at least one ofthe at least one users' evaluation of the presented data.
 9. A methodaccording to claim 8, where the at least one of the at least one usersinput includes at least one of: a rank of the measured at least oneresponse, a rating of the measured at least one response, one or morefitness values, a selection of the measured at least one response, aselection of a feature of the measured at least one response, atermination of the method, an identification of parents for a geneticalgorithm, at least one constraint, a modification of at least oneconstraint, a modification of at least one genetic operator, and aspecification of at least one genetic operator.
 10. A method accordingto claim 8, where the method is terminated based on the at least one ofthe at least one users input.
 11. A method according to claim 1, wheremeasuring at least one response of the external system includes at leastone of: through at least one of the at least one output devices,presenting data to at least one user based on the measured at least oneresponse in parallel, and through at least one of the at least oneoutput devices, presenting data to at least one user based on themeasured at least one response in sequential order.
 12. A methodaccording to claim 1, where applying at least one genetic operatorincludes: ranking the measured at least one response based on acomparison to a metric, and, applying the at least one genetic operatorbased on the ranking.
 13. A method according to claim 1, where applyingat least one genetic operator includes applying at least one constraintto at least one of the genotypes.
 14. A method according to claim 13,where applying at least one constraint includes weighting the at leastone constraint.
 15. A method according to claim 1, where the externalsystem vulnerability includes at least one of: at least one externalsystem error, at least one external system defect, at least one externalsystem loophole, and at least one external system weakness.
 16. Acomputer-readable medium having computer-readable instructions storedthereon which, as a result of being executed in a computer system havingat least one user interface including at lest one output device and atleast one input device, instruct the computer system to perform amethod, comprising: a) receiving through at least one of the at leastone input devices input with respect to a plurality of parametersrelating to the external system; b) based upon the input received,generating in the computer system a population of genotypes, thegenotypes based on at least one stimulus to the external system, c)measuring at least one response of the external system upon providingthe population of genotypes to at least one model of the externalsystem, d) based on the measured at least one response of the externalsystem not revealing a vulnerability of the external system, applying atleast one genetic operator to at least some of the population ofgenotypes, and e) based on the measured at least one response of theexternal system revealing a vulnerability of the external system,associating the said vulnerability of the external system with at leastone of the population of genotypes, and causing the said vulnerabilityto be presented to at least one user through at least one of the atleast one output devices.
 17. A medium according to claim 16, whereapplying at least one genetic operator includes applying at least oneof: selection, crossover, mutation, deletion, diversity injection, andelitism.
 18. A medium according to claim 16, where applying at least onegenetic operator includes implementing elitism by: through at least oneof the at least one output devices, presenting at least two graphicalrepresentations to at least one of the at least one users, each of theat least two graphical representations associated with at least onegenotype in the population and the at least one of the measuredresponses, through at least one of the at least one input devices,receiving a selection of at least one of the graphical representationsfrom at least one of the at least one users, and, identifying at leastone genotype associated with the at least one selected graphicalrepresentation, and returning to generating a population of genotypesincluding the identified at least one genotype.
 19. A medium accordingto claim 16, where applying at least one genetic operator includesimplementing elitism by: comparing the measured at least one response toa measure, and, based on the comparison, identifying at least onegenotype, and, returning to generating a population of genotypesincluding the identified at least one genotype.
 20. A medium accordingto claim 16, where based on the measured at least one response of theexternal system revealing a vulnerability of the external system,associating the said vulnerability of the external system with at leastone of the population of genotypes includes: comparing the measured atleast one response to at least one threshold, and, determining thevulnerability based on the comparison.
 21. A medium according to claim16, where measuring at least one response of the external systemincludes comparing the measured at least one response to a metric.
 22. Amedium according to claim 16, where measuring at least one response ofthe external system includes comparing the measured at least oneresponse to at least one of a fitness function and an objectivefunction.
 23. A medium according to claim 16, where measuring at leastone response of the external system includes: determining that anobjective function is mathematically unexpressed, through at least oneof the at least one output devices, presenting data based on themeasured at least one response of the external system to at least one ofthe at least one users, and, through at least one of the at least oneinput devices, receiving at least one input from the at least one of theat least one users, the at least one input based on the at least one ofthe at least one users' evaluation of the presented data.
 24. A mediumaccording to claim 23, where the at least one of the at least one usersinput includes at least one of: a rank of the measured at least oneresponse, a rating of the measured at least one response, one or morefitness values, a selection of the measured at least one response, aselection of a feature of the measured at least one response, atermination of the method, an identification of parents for a geneticalgorithm, at least one constraint, a modification of at least oneconstraint, a modification of at least one genetic operator, and aspecification of at least one genetic operator.
 25. A medium accordingto claim 23, where the method is terminated based on the at least one ofthe at least one users input.
 26. A medium according to claim 16, wheremeasuring at least one response of the external system includes at leastone of: through at least one of the at least one output devices,presenting data to at least one user based on the measured at least oneresponse in parallel, and through at least one of the at least one inputdevices, presenting data to at least one user based on the measured atleast one response in sequential order.
 27. A medium according to claim16, where applying at least one genetic operator includes: ranking themeasured at least one response based on a comparison to a metric, and,applying the at least one genetic operator based on the ranking.
 28. Amedium according to claim 16, where applying at least one geneticoperator includes applying at least one constraint to at least one ofthe genotypes.
 29. A medium according to claim 28, where applying atleast one constraint includes weighting the at least one constraint. 30.A medium according to claim 16, where the external system vulnerabilityincludes at least one of: at least one external system error, at leastone external system defect, at least one external system loophole, andat least one external system weakness.